A mean-field opinion model on hypergraphs: From modeling to inference

发布时间:2024-06-20 点击次数:

标题:A mean-field opinion model on hypergraphs: From modeling to inference






  The perspectives and opinions of people change and spread through social interactions on a daily basis. In the study of opinion dynamics, one often models social entities (such as Facebook accounts) as nodes and their relationships (such as friendships) as edges, and examines how opinions evolve as dynamical processes on networks, including graphs, hypergraphs, multi-layer networks, etc. In the first part of my talk, I will introduce a model of opinion dynamics and derive its mean-field limit as the total number of agents goes to infinity. The mean-field opinion density satisfies a kinetic equation of Kac type. We prove properties of the solution of this equation, including nonnegativity, conservativity, and steady-state convergence. The parameters of such opinion models play a nontrivial role in shaping the dynamics and can also be in the form of functions. In reality, it is often impractical to measure these parameters directly. In the second part of the talk, I will approach the problem from an inverse perspective and present how to infer the parameters from limited partial observations. I will provide sufficient conditions of measurement for two scenarios, such that one is able to identify the parameters uniquely. I will also provide a numerical algorithm of the inference when the data set only has a limited number of data points.